In the commercial production of the element arsenic, arsenic (II) oxide is heated with carbon which reduces the oxide to the metal according to the following equation: 2As2O3 + 3C ----„³ 3CO2 +4As
A>if 8.87 g of As2O3 is used in the reaction and 5.33 g of As is produced what is the percentage yield?
B>If 67 of carbon is used up in a different reaction and 425 g of As is produced, calculate the percentage yield of this reaction
A. You have the balanced equation.
1. Convert 8.87 g As2O3 to mols remembering that mols = grams/molar mass.
2. Using the coefficients in the balanced equation, convert mols As203 to mols As.
3. Convert mols As to grams. grams = mols x molar mass. This is the theoretical yield.
4. %yield =
(actual yield/theoretical yield)x 100
B. The procedure is the same for this part of the problem but you start with carbon. Post your work if you get stuck.
79.3%
To calculate the percentage yield of a reaction, we need to compare the actual yield to the theoretical yield and then calculate the percentage.
A) First, let's calculate the theoretical yield of As in this reaction. We are given that 8.87 g of As2O3 is used.
The molar mass of As2O3 is 197.84 g/mol, so we can calculate the number of moles of As2O3 used:
Moles of As2O3 = Mass of As2O3 / Molar mass of As2O3
Moles of As2O3 = 8.87 g / 197.84 g/mol
Moles of As2O3 = 0.0448 mol
From the balanced chemical equation, we can see that the stoichiometric ratio between As2O3 and As is 2:4 or 1:2.
Therefore, the number of moles of As produced is twice the number of moles of As2O3 used:
Moles of As = 2 * Moles of As2O3
Moles of As = 2 * 0.0448 mol
Moles of As = 0.0896 mol
Now, we can calculate the theoretical yield of As:
Theoretical yield of As = Moles of As * Molar mass of As
Theoretical yield of As = 0.0896 mol * 74.92 g/mol
Theoretical yield of As = 6.71 g
The percentage yield is then calculated by dividing the actual yield by the theoretical yield and multiplying by 100:
Percentage yield = (Actual yield / Theoretical yield) * 100
Percentage yield = (5.33 g / 6.71 g) * 100
Percentage yield = 79.5%
B) In this case, we are given that 67 g of carbon is used up and 425 g of As is produced. We need to calculate the percentage yield.
First, we need to find the number of moles of carbon used:
Moles of C = Mass of C / Molar mass of C
Moles of C = 67 g / 12.01 g/mol
Moles of C = 5.58 mol
From the balanced chemical equation, we can see that the stoichiometric ratio between C and As is 3:4. Therefore, the number of moles of As produced is:
Moles of As = (4/3) * Moles of C
Moles of As = (4/3) * 5.58 mol
Moles of As = 7.45 mol
Now, let's calculate the theoretical yield of As:
Theoretical yield of As = Moles of As * Molar mass of As
Theoretical yield of As = 7.45 mol * 74.92 g/mol
Theoretical yield of As = 557 g
The percentage yield is then calculated by dividing the actual yield by the theoretical yield and multiplying by 100:
Percentage yield = (Actual yield / Theoretical yield) * 100
Percentage yield = (425 g / 557 g) * 100
Percentage yield = 76.3%
To find the percentage yield of the reaction, you need to compare the actual yield (the amount of As produced) to the theoretical yield (the amount of As that would be produced if the reaction went perfectly).
A. To calculate the theoretical yield:
1. Convert the mass of As2O3 to moles. Use the molar mass of As2O3, which is 197.841 g/mol.
- Moles of As2O3 = mass of As2O3 / molar mass of As2O3
Moles of As2O3 = 8.87 g / 197.841 g/mol
2. Use stoichiometry to find the moles of As produced. According to the balanced equation, the mole ratio of As2O3 to As is 2:4.
So, moles of As = 2 * (moles of As2O3 / 2)
Moles of As = (8.87 g / 197.841 g/mol) * 2/2
3. Convert the moles of As to grams by multiplying by the molar mass of As, which is 74.92160 g/mol.
Theoretical yield of As = moles of As * molar mass of As
Theoretical yield of As = [(8.87 g / 197.841 g/mol) * 2/2] * 74.92160 g/mol
B. Repeat the same steps to calculate the theoretical yield for the second reaction.
1. Convert the mass of carbon to moles. Use the molar mass of carbon, which is 12.01 g/mol.
Moles of carbon = mass of carbon / molar mass of carbon
Moles of carbon = 67 g / 12.01 g/mol
2. Use stoichiometry to find the moles of As produced. According to the balanced equation, the mole ratio of carbon to As is 3:4.
So, moles of As = 4/3 * moles of carbon
Moles of As = 4/3 * (67 g / 12.01 g/mol)
3. Convert the moles of As to grams by multiplying by the molar mass of As, which is 74.92160 g/mol.
Theoretical yield of As = moles of As * molar mass of As
Theoretical yield of As = [4/3 * (67 g / 12.01 g/mol)] * 74.92160 g/mol
To calculate the percentage yield, divide the actual yield by the theoretical yield and multiply by 100.
A. Percentage yield = (actual yield / theoretical yield) * 100
Percentage yield = (5.33 g / [(8.87 g / 197.841 g/mol) * 2/2] * 74.92160 g/mol) * 100
B. Percentage yield = (425 g / [4/3 * (67 g / 12.01 g/mol)] * 74.92160 g/mol) * 100
After calculating these expressions, you will get the respective percentage yields for the reactions.